A Hierarchical Transitive-Aligned Graph Kernel for Un-attributed Graphs

In this paper, we develop a new graph kernel, namely the Hierarchical Transitive-Aligned kernel, by transitively aligning the vertices between graphs through a family of hierarchical prototype graphs. Comparing to most existing state-of-the-art graph kernels, the proposed kernel has three theoretical advantages. First, it incorporates the locational correspondence information between graphs into the kernel computation, and thus overcomes the shortcoming of ignoring structural correspondences arising in most R-convolution kernels. Second, it guarantees the transitivity between the correspondence information that is not available for most existing matching kernels. Third, it incorporates the information of all graphs under comparisons into the kernel computation process, and thus encapsulates richer characteristics. By transductively training the C-SVM classifier, experimental evaluations demonstrate the effectiveness of the new transitive-aligned kernel. The proposed kernel can outperform state-of-the-art graph kernels on standard graph-based datasets in terms of the classification accuracy

A Survey on Graph Kernels

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification

Neural correlates of consciousness in the complexity of brain networks

How do we define consciousness? Besides philosophical endeavours, the development of modern neuroimaging techniques fostered a principled way of quantifying the neural correlates of consciousness. Acquiring and analysing resting-state functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) data, has allowed neuroscientists to noninvasively map the brain’s functional interactions (or functional connectivity). Based on data obtained during controlled loss of consciousness and in cases of patients with disorders of consciousness, it has now been suggested that multiple, functionally specialized/segregated areas need to interact and integrate information in order to support consciousness. Thus an emerging idea in neuroscience is that the brain needs to balance the coexistence of functional segregation and integration, a property often termed as brain complexity, in order to produce consciousness. A resulting hypothesis is that consciousness is abolished when the balance between segregation and integration is lost and brain complexity is attenuated. In that regard, I use complexity of functional connectivity, an aggregate measure of segregation and integration, as a marker of consciousness. This effort consists of two parts. First, I provide evidence that complexity in the healthy, awake brain is critical in the sense that it reflects a critical balance of segregation and integration designed to support efficient information communication. In turn, I provide evidence that loss of consciousness is associated with decreased complexity i.e. that functional connectivity departs from the critical complexity of the healthy, awake brain towards a more segregated configuration. The structure of this thesis follows accordingly. In the first experimental chapter (3), I show the importance of the critical balance of complexity in the healthy, awake brain by using a structure-to-function association model. Specifically, I show that complexity can be derived upon certain optimal, structural connections (computed as the Nash equilibrium between regions), which promote efficient communication in the brain from the regional to the whole-brain level. Chapter 4 focuses on capturing alterations of complexity in cases of sedation, anaesthesia and disorders of consciousness. Specifically, I show that as one goes from the awake state to anaesthetic-induced unconsciousness and disorders of consciousness, functional connectivity becomes less complex and more segregated. A refined approach that quantifies complexity in different parts of the brain allowed me to see whether this reduction in complexity is more evident in specific regions and networks. Under this framework, at the regional level I provide evidence that sparsely connected regions linking different parts of the brain play a critical role in whole-brain complexity. At the network level I show the importance of the default mode network in whole-brain complexity. Even during rest, the brain is not static and displays rich temporal dynamics. Thus it is not only the complexity at each snapshot of time but also how complexity changes across time that can help us understand loss of consciousness. In chapter 5 I use a dynamic framework to derive and characterize the dynamics of functional connectivity during loss of consciousness. In turn, I provide evidence that brains become less temporally complex as one goes from the awake state to anaesthetic-induced unconsciousness and disorders of consciousness. Moreover, my goal is to see whether the principle of complexity reduction can be also applied to the developing brain. Towards this direction, in chapter 6 I use complexity on EEG connectivity data to examine anaesthetic-induced loss of consciousness in infants. Specifically, I show that complexity in anaesthetised infants aged 0-3 years is reduced compared to a state of emergence from anaesthesia, indicating its importance in supporting consciousness and brain function since infancy. Taken together, these findings show that while the complexity of the healthy, awake brain during rest is critically configured, the unconscious brain is characterized by reduced complexity. Based on the results presented in this work, I propose that consciousness can be assessed on the basis of complexity of resting-state functional connectivity data